Question

find the value of A and B in each of the following (i) 5+2√3/7+4√3 =a-6√3

Answer 1

Heya there !!!
Here is the answer you were looking for :

Identity used :

$(x + y)(x - y) = {x}^{2} - {y}^{2}$


$\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } = a - 6 \sqrt{3}$

In L.H.S.

On rationalizing the denominator we get,

$= \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } \\ \\ = \frac{5(7 - 4 \sqrt{3} )+2 \sqrt{3}(7 - 4 \sqrt{3}) }{ {(7)}^{2} - {4 \sqrt{3} )}^{2} } \\ \\ = \frac{35 - 20 \sqrt{3} + 14 \sqrt{3} - 24}{49 - 48} \\ \\ = 11 - 6 \sqrt{3}$

On comparing we get,

$11 - 6 \sqrt{3} = a - 6 \sqrt{3} \\ \\ a = 11$

Hope this helps!!!

Thanks...
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Answer 2

Heya____!!!!

Here's your answer____=>=>=>

Refer to the attached file____^^^

Value of a = 11____^_^

Hope it will help you____##

Thanks____☆▪☆